Converting PNG to EPS

Hi everyone, I am trying to convert a bunch of PNG logos for a school into EPS files. The school's logo has a heavy white stroke around the logo and every time I do image trace>expand>ungroup, the white stroke ends up being selected to the background and then I am only left with the red words without the white stroke around them... 

If anyone has a better idea of how to convert this type of logo to an EPS without losing the white stroke/outline I am all ears.